Question

If the vector components of a vector \(\vec a\) along a vector \[ \vec b=4\hat i+5\hat j+3\hat k \] and perpendicular to \(\vec b\) are respectively \[ \frac{7}{25}(4\hat i+5\hat j+3\hat k) \] and \[ \frac{1}{25}(47\hat i-10\hat j-46\hat k), \] then \[ |\vec a|^2= \]

• A. \(6\)
• B. \(9\)
• C. \(11\)
• D. \(17\)

Hint:

When a vector is expressed as the sum of components parallel and perpendicular to another vector, the components are orthogonal. Therefore, use \( |\vec a|^2=|\vec a_{\parallel}|^2+|\vec a_{\perp}|^2 \).

Answer 1

The Correct Option is C